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 Hypergeometric2F1

 http://functions.wolfram.com/07.23.03.bytf.01

 Input Form

 Hypergeometric2F1[3/8, 2, 35/8, -z] == -((1/(65536 z^(27/8))) (171 (-1)^(1/8) (1672 (-1)^(7/8) z^(3/8) + 2448 (-1)^(7/8) z^(11/8) + 264 (-1)^(7/8) z^(19/8) - 33 I (1 + z)^2 (-19 + 5 z) Log[1 - (-1)^(1/8) z^(1/8)] + 33 I (1 + z)^2 (-19 + 5 z) Log[1 + (-1)^(1/8) z^(1/8)] - 627 (-1)^(3/4) Log[1 - (-1)^(3/8) z^(1/8)] - 1089 (-1)^(3/4) z Log[1 - (-1)^(3/8) z^(1/8)] - 297 (-1)^(3/4) z^2 Log[1 - (-1)^(3/8) z^(1/8)] + 165 (-1)^(3/4) z^3 Log[1 - (-1)^(3/8) z^(1/8)] + 627 (-1)^(3/4) Log[1 + (-1)^(3/8) z^(1/8)] + 1089 (-1)^(3/4) z Log[1 + (-1)^(3/8) z^(1/8)] + 297 (-1)^(3/4) z^2 Log[1 + (-1)^(3/8) z^(1/8)] - 165 (-1)^(3/4) z^3 Log[1 + (-1)^(3/8) z^(1/8)] - 627 Log[1 - (-1)^(5/8) z^(1/8)] - 1089 z Log[1 - (-1)^(5/8) z^(1/8)] - 297 z^2 Log[1 - (-1)^(5/8) z^(1/8)] + 165 z^3 Log[1 - (-1)^(5/8) z^(1/8)] + 627 Log[1 + (-1)^(5/8) z^(1/8)] + 1089 z Log[1 + (-1)^(5/8) z^(1/8)] + 297 z^2 Log[1 + (-1)^(5/8) z^(1/8)] - 165 z^3 Log[1 + (-1)^(5/8) z^(1/8)] + 627 (-1)^(1/4) Log[1 - (-1)^(7/8) z^(1/8)] + 1089 (-1)^(1/4) z Log[1 - (-1)^(7/8) z^(1/8)] + 297 (-1)^(1/4) z^2 Log[1 - (-1)^(7/8) z^(1/8)] - 165 (-1)^(1/4) z^3 Log[1 - (-1)^(7/8) z^(1/8)] - 627 (-1)^(1/4) Log[1 + (-1)^(7/8) z^(1/8)] - 1089 (-1)^(1/4) z Log[1 + (-1)^(7/8) z^(1/8)] - 297 (-1)^(1/4) z^2 Log[1 + (-1)^(7/8) z^(1/8)] + 165 (-1)^(1/4) z^3 Log[1 + (-1)^(7/8) z^(1/8)])))

 Standard Form

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 MathML Form

 2 F 1 ( 3 8 , 2 ; 35 8 ; - z ) TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox["\[InvisiblePrefixScriptBase]", "2"], SubscriptBox["F", "1"]]], "\[InvisibleApplication]", RowBox[List["(", RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox["3", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], ",", TagBox["2", HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[TagBox[TagBox[FractionBox["35", "8"], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], HypergeometricPFQ, Rule[Editable, False], Rule[Selectable, False]], ";", TagBox[RowBox[List["-", "z"]], HypergeometricPFQ, Rule[Editable, True], Rule[Selectable, True]]]], ")"]]]], InterpretTemplate[Function[HypergeometricPFQ[Slot[1], Slot[2], Slot[3]]]], Rule[Editable, False], Rule[Selectable, False]], HypergeometricPFQ] - 1 65536 z 27 / 8 ( 171 - 1 8 ( 165 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 3 - 165 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 3 + 165 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 3 - 165 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 3 - 165 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 3 + 165 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 3 + 264 ( - 1 ) 7 / 8 z 19 / 8 - 297 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z 2 + 297 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z 2 - 297 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z 2 + 297 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z 2 + 297 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z 2 - 297 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z 2 + 2448 ( - 1 ) 7 / 8 z 11 / 8 - 1089 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) z + 1089 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) z - 1089 log ( 1 - ( - 1 ) 5 / 8 z 8 ) z + 1089 log ( ( - 1 ) 5 / 8 z 8 + 1 ) z + 1089 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) z - 1089 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) z + 1672 ( - 1 ) 7 / 8 z 3 / 8 - 33 ( z + 1 ) 2 ( 5 z - 19 ) log ( 1 - - 1 8 z 8 ) + 33 ( z + 1 ) 2 ( 5 z - 19 ) log ( - 1 8 z 8 + 1 ) - 627 ( - 1 ) 3 / 4 log ( 1 - ( - 1 ) 3 / 8 z 8 ) + 627 ( - 1 ) 3 / 4 log ( ( - 1 ) 3 / 8 z 8 + 1 ) - 627 log ( 1 - ( - 1 ) 5 / 8 z 8 ) + 627 log ( ( - 1 ) 5 / 8 z 8 + 1 ) + 627 - 1 4 log ( 1 - ( - 1 ) 7 / 8 z 8 ) - 627 - 1 4 log ( ( - 1 ) 7 / 8 z 8 + 1 ) ) ) HypergeometricPFQ 3 8 2 35 8 -1 z -1 1 65536 z 27 8 -1 171 -1 1 8 165 -1 3 4 1 -1 -1 3 8 z 1 8 z 3 -1 165 -1 3 4 -1 3 8 z 1 8 1 z 3 165 1 -1 -1 5 8 z 1 8 z 3 -1 165 -1 5 8 z 1 8 1 z 3 -1 165 -1 1 4 1 -1 -1 7 8 z 1 8 z 3 165 -1 1 4 -1 7 8 z 1 8 1 z 3 264 -1 7 8 z 19 8 -1 297 -1 3 4 1 -1 -1 3 8 z 1 8 z 2 297 -1 3 4 -1 3 8 z 1 8 1 z 2 -1 297 1 -1 -1 5 8 z 1 8 z 2 297 -1 5 8 z 1 8 1 z 2 297 -1 1 4 1 -1 -1 7 8 z 1 8 z 2 -1 297 -1 1 4 -1 7 8 z 1 8 1 z 2 2448 -1 7 8 z 11 8 -1 1089 -1 3 4 1 -1 -1 3 8 z 1 8 z 1089 -1 3 4 -1 3 8 z 1 8 1 z -1 1089 1 -1 -1 5 8 z 1 8 z 1089 -1 5 8 z 1 8 1 z 1089 -1 1 4 1 -1 -1 7 8 z 1 8 z -1 1089 -1 1 4 -1 7 8 z 1 8 1 z 1672 -1 7 8 z 3 8 -1 33 z 1 2 5 z -19 1 -1 -1 1 8 z 1 8 33 z 1 2 5 z -19 -1 1 8 z 1 8 1 -1 627 -1 3 4 1 -1 -1 3 8 z 1 8 627 -1 3 4 -1 3 8 z 1 8 1 -1 627 1 -1 -1 5 8 z 1 8 627 -1 5 8 z 1 8 1 627 -1 1 4 1 -1 -1 7 8 z 1 8 -1 627 -1 1 4 -1 7 8 z 1 8 1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2007-05-02